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Zeitschrift für Analysis und ihre Anwendungen

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Volume 35, Issue 1, 2016, pp. 21–39
DOI: 10.4171/ZAA/1553

Published online: 2015-12-23

Nonautonomous Dynamics with Discrete Time and Topological Equivalence

Luis Barreira[1], Liviu Horia Popescu[2] and Claudia Valls[3]

(1) Instituto Superior Técnico, Lisboa, Portugal
(2) Oradea University, Romania
(3) Instituto Superior Técnico, Lisboa, Portugal

For evolution families with discrete time, we show that any exponential dichotomy is topologically equivalent to a certain normal form, in which the exponential behavior along the stable and unstable directions are multiples of the identity. We consider the general case of a generalized exponential dichotomy in which the usual exponential behavior is replaced by an arbitrary growth rate. In addition, we show that the topological equivalence between two evolution families with generalized exponential dichotomies can be completely characterized in terms of a notion of equivalence between the growth rates.

Keywords: Strong exponential dichotomies, topological equivalence

Barreira Luis, Popescu Liviu Horia, Valls Claudia: Nonautonomous Dynamics with Discrete Time and Topological Equivalence. Z. Anal. Anwend. 35 (2016), 21-39. doi: 10.4171/ZAA/1553